本課程專注於對李群理論的介紹，尤其側重於它同微分幾何之間的聯繫。本課程選用的教材是《微分幾何、李群和對稱空間》（Sigurdur Helgason著，美國數學協會，2001年版）。
This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001).
本課程的內容主要基於教材第一章的前半部分和第二章。然而課程還將簡單介紹了基本的黎曼幾何和複流形的知識，並會詳細討論半單李群和對稱空間的理論。
Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.
